C++ for Scientists - Technische Universität Dresden

4.8. FUNCTORS 111
vector x(3), y(4);
v= w;
x= y;
The last two lines are incompatible vector assignments. The difference is that the imcompatibility
in the second assignment x= y; is discovered at run time in our assertion. The assignment
v= w; does not even compile because fixed-size vectors of dimension 3 only accept vectors of the
same dimension as argument.
Like type arguments, non-type template arguments can have defaults. Say the most frequent
dimension of our vectors is three because we live in a three-dimensional world, relativity and
string theory aside. Then we save some typing with a default:
template
class fsize vector
{ /∗ ... ∗/ };
fsize vector v, w, x, y;
fsize vector space time;
fsize vector string;
4.8 Functors
Let us develop a mathematical algorithm for computing the finite difference of a differentiable
function f. The finite difference is an approximation of the first derivative by
f ′ (x) ≈
where h is a small value also called spacing.
f(x + h) − f(x)
h
A general function for computing the finite difference is presented here:
#include
#include
// Function taking a function argument
double finite difference( double f( double ), double x, double h ) {
return ( f(x+h) − f(x) ) /h ;
}
double sin plus cos( double x ) {
return sin(x) + cos(x) ;
}
int main() {
std::cout ≪ finite difference( sin plus cos, 1., 0.001 ) ≪ std::endl ;
std::cout ≪ finite difference( sin plus cos, 0., 0.001 ) ≪ std::endl ;
}